First, I’ve never taken a physics class or attended highschool before, hence the ELI5. I’ve read many explanations but it doesn’t really make intuitive sense to me. For example (assuming there’s no air resistance / drag), let’s say I was traveling in a car going 120 mph and I wanted to decelerate to 90 mph. This would take four times as much energy than going from 30 mph to 0.
But let’s say there were two cars traveling at 120 mph. The car next to me decelerates to 90 mph, but I’m still going 120. From my point of view, the car next to me just started going 30 mph in the opposite direction. Why would this require 4 times as much energy than if both cars were just stationary, and the car next to me actually started going 30 mph in the opposite direction?
And, let’s say we’re both standing on earth. One person at the north pole and one at the equator. Both of us throw a ball, but the ball at the equator is already traveling at something like 1,000 mph due to the earth’s rotation. Shouldn’t throwing a ball eastward then require way more energy to go from 1,000 to say 1,020 mph, than the person throwing the ball at the north pole who just has to accelerate it from 0 mph to 20 mph?
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> let’s say I was traveling in a car going 120 mph and I wanted to decelerate to 90 mph. This would take four times as much energy than going from 30 mph to 0.
> But let’s say there were two cars traveling at 120 mph. The car next to me decelerates to 90 mph, but I’m still going 120. From my point of view, the car next to me just started going 30 mph in the opposite direction. Why would this require 4 times as much energy than if both cars were just stationary, and the car next to me actually started going 30 mph in the opposite direction?
This is a really fascinating question. And the answer takes a bit of thinking about, but you’ve already got the basics of it.
In classical mechanics (pre-20th century) energy is a mathematical tool that is useful in figuring out how things interact. It corresponds to how much something has been forced. The more it has been forced, the more energy it has gained. Because forces are symmetric (Newton’s Third Law) the more one thing has been forced, the more other things have forced things; so we can factor this into energy. If one thing has been forced and so gained “been forced stuff” (energy) we can say that the things that forced it have lost “been forced stuff.” We get conservation of energy!
If energy is conserved that can be really useful for understanding situations. Rather than having to worry about all the forces and interactions going on at each moment in some system, we can look at the energy at the start, look at the energy at the end, and you can get a great idea of what is happening.
Anyway. The important thing to note about this is that it is a maths thing; helpful, but has limitations. One of the big ones is that it depends on our frame of reference (which is what you’ve noticed). It isn’t absolute, but relative. But that’s Ok as we’re only ever looking at how it changes, and it just means we have to be careful about switching between reference frames when doing energy calculations (but we should be doing that anyway).
So let’s look at your situation.
Your car is going at 120mph. It want to decelerate to 90mph. That would involve losing more energy than you’d have to lose to decelerate from 90mph to 60mph, and 4 times as much energy as it would take for you to decelerate from 30mph to 0mph. But this is all from a reference frame fixed with the ground.
From *your* point of view, though, you’re at rest. You’re not changing speed, so no need for any change in energy at all! Of course, you’re in a non-inertial reference frame, so the maths gets a bit weird, but this is a good indication that something weird is going on.
So let’s look at another point of view. Some car that was travelling at the same speed as you before you started slowing down.
From their point of view you were going at 0mph, then *sped up* to 30mph (backwards), then sped up further to 60mph and eventually up to 120mph. From their point of view *you have gained energy*! This is getting really weird…
The big thing we’re missing is that energy is being transferred; if something is gaining or losing energy, something else must be losing or gaining it. We’re only looking at half the problem.
Let’s massively oversimplify the problem and assume that as you slow down you are dumping energy into the Earth. Conservation of momentum tells us that as you slow down the Earth must speed up. So from our “with the ground” frame of reference, the Earth will be gaining energy as you lose energy.
But from the other car’s point of view, as you “speed up” the Earth will “slow down,” so as you gain energy, the Earth loses energy. Which is what we expect.
The maths gets a bit messy (and we have to worry about whole systems for conservation of momentum and conservation of energy) but it all works out in the end. Provided we do *everything* (including measuring distances and forces) from the just one reference frame. The calculations will be different and give us different changes in energy, depending on which reference frame we use, but we will get the same overall result for how things move.
Oddly enough, this is kind of how E = mc^2 was first derived; by looking at how energy changes work when viewed from different reference frames. Einstein’s paper on it is only a couple of pages and is a simple thought experiment.
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